Empirical EQ calibration via 2-tone comparisons
Nov 30, 2020 at 6:43 PM Thread Starter Post #1 of 7

jshaevitz

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(I am not sure if this has been covered before, please point me in the right direction if it has.)

I like treble forward headphones and have always found neutral and warm cans to sound extremely veiled. Looking at published frequency response graphs I've always thought to myself, "That's just not what it sounds like to me." My Grados always sound much more realistic than other headphones (as a musician I do think I know what certain instruments sound like in real life). An enhanced treble response always sounds more real to me with headphones. If I tried to EQ my favorite cans to a measured flat response the result was always horrible to my ears.

The underlying perceived frequency response is quite complicated and combines the driver/housing but also the shape of the ear, the physical properties of the ear drum/cochlea, auditory cortex etc. I know that some headphone measuring instruments are meant to emulate these but everyone's ear are different, physically, mechanically, and neurally. So I thought up a way to test my perceived frequency response using my Grado GS3000e. The basic idea is to compare the perceived amplitude of two tones and do this over the audible spectrum. As a first pass I used the OSX 31-band AUGraphicEQ to adjust each band until I thought it matched the amplitude of a 1kHz sine wave. I wrote a program to alternate between the two pitches (the test pitch and 1kHz) every 0.5 seconds a number of times and I would adjust that band on the EQ with my eyes closed until the levels seemed to match. (Note, 16kHz and 20kHz were not produced reliably by my program so I set those to 0dB).

My results are shown in the graphic below with my empirical levels in blue and the published curve from reference-audio-analyzer.pro in red. As you can see, my perception is much flatter than the measured curve. I obviously don't know why at this point, but I think this explains my observation that treble-forward headphones sound more real and 'flat' to me compared to neutral cans that "measure flat".

Grado3ke Emperical Calibration.jpg


There are obviously many things scientifically unsound about how I carried out this measurement (I am a scientist in real life) but I think the general idea is sound. I could even imagine a simple software tool that really made this very simple. I am curious to hear the thoughts of others on this.
 
Nov 30, 2020 at 7:50 PM Post #2 of 7
I can re-use once again something I once wrote in another context but is also relevant in this case, it explains how it could indeed very well be possible that treble-forward headphones sound more real and 'flat' to you.
with headphones there is one complication: there is no objective flat or neutral for everyone.
If you are listening to sounds coming from your environment, from a distance, then the sound is subjected to your personal head related transfer function (hrtf) filtering. (The sound is bouncing off your torso, bending round your head, bouncing of your pinnae, bending into your ear canal, etc.)
The resulting filtering of the audio differs per person. If you use headphones a part of this filtering is skipped. Because the part that is skipped differs per person one and the same headphone will sound objectively different to different people.
 
Dec 1, 2020 at 12:27 AM Post #4 of 7
Yes on individual variations:
Screenshot 2020-12-01 053250.png


No on flatness:
By seeking equal loudness with 1kHz reference, the result isn't really flat. If you do it normally(strictly trying to match the perceived loudness between the 2 tones) you get the EQ you need for your equal loudness contour at that listening level on that headphone. A headphone EQed that way would not sound flat when listening to most musics.

The perception of neutral headphone is a little different and requires to pick some known reference. Maybe some experience of sweeps or tones played on calibrated speaker(if that's what FR you wish to emulate). Then you can consciously try to get the variation you felt between 2 tones on the speaker, while using your headphone with EQ.
Or you can consider some real instrument, but then you might have 2 problems. Where you're used to hear it, against where the mic was placed when recording it. And of course whatever processing and EQ that might have been applied when making the album(if the mic was even flat to begin with).
In general the quest for a flat reference is a philosophical exercise in and of itself for headphones. One fairly objective method consists in getting the equal loudness contour like how you suggest with 2 tones and trying to match them before moving to the next frequency. And then repeat the same exercise on calibrated speakers. With those 2 EQ you can sort out what you need applied on your headphone. But even that is a little flawed because when we listen to music on headphones, we don't get the room reverb and stereo of speaker playback. Those differences are likely to make our subjective headphone impressions(and preferences) deviate some more.
 
Dec 1, 2020 at 8:04 AM Post #5 of 7
Yes on individual variations:
Screenshot 2020-12-01 053250.png

No on flatness:
By seeking equal loudness with 1kHz reference, the result isn't really flat. If you do it normally(strictly trying to match the perceived loudness between the 2 tones) you get the EQ you need for your equal loudness contour at that listening level on that headphone. A headphone EQed that way would not sound flat when listening to most musics.

The perception of neutral headphone is a little different and requires to pick some known reference. Maybe some experience of sweeps or tones played on calibrated speaker(if that's what FR you wish to emulate). Then you can consciously try to get the variation you felt between 2 tones on the speaker, while using your headphone with EQ.
Or you can consider some real instrument, but then you might have 2 problems. Where you're used to hear it, against where the mic was placed when recording it. And of course whatever processing and EQ that might have been applied when making the album(if the mic was even flat to begin with).
In general the quest for a flat reference is a philosophical exercise in and of itself for headphones. One fairly objective method consists in getting the equal loudness contour like how you suggest with 2 tones and trying to match them before moving to the next frequency. And then repeat the same exercise on calibrated speakers. With those 2 EQ you can sort out what you need applied on your headphone. But even that is a little flawed because when we listen to music on headphones, we don't get the room reverb and stereo of speaker playback. Those differences are likely to make our subjective headphone impressions(and preferences) deviate some more.

@castleofargh Thank you for the detailed response. Some questions:
  1. You write, "A headphone EQed that way would not sound flat when listening to most musics." Why do you say this? Is there data to back this up?
  2. The figure you sent is very nice, I will go and read the original references. These curves measure the effect of the ear/head shape and mechanics on sound entering the entrance to the auditory canal. Do you know of any references that look at subjective loudness curves? I am particularly interested in any work looking at differences in mechanics of the tympanic or cochlear basilar membranes which should effect the detection of different frequencies.
 
Dec 3, 2020 at 8:11 PM Post #6 of 7
You write, "A headphone EQed that way would not sound flat when listening to most musics." Why do you say this? Is there data to back this up?
Look up "Equal-Loudness Contours" or "Fletcher-Munson Curves" and try to think of its consequences.
Your (and everyone's) ears' sensitivity is depending on the frequencies and the contour describes this dependency. For example, you need a bigger SPL at 20Hz than at 1kHz to perceive a similar loudness between them. Basically, if you match loudness by ear what you are getting is going to have a massive bass boost and some dip around the 2-4kHz region.
 
Dec 4, 2020 at 2:16 AM Post #7 of 7
@castleofargh Thank you for the detailed response. Some questions:
  1. You write, "A headphone EQed that way would not sound flat when listening to most musics." Why do you say this? Is there data to back this up?
  2. The figure you sent is very nice, I will go and read the original references. These curves measure the effect of the ear/head shape and mechanics on sound entering the entrance to the auditory canal. Do you know of any references that look at subjective loudness curves? I am particularly interested in any work looking at differences in mechanics of the tympanic or cochlear basilar membranes which should effect the detection of different frequencies.
sorry I must have checked your post rapidly, planning to come back to you, and forgot. what @VNandor said. our hearing system isn't SPL flat over frequencies as the body changes the response:
Ear-resonance.jpg

It's one model, as mentioned not so clearly, it's for sound presented at a 45° angle on the horizontal axis. Your own body can be a little different here and there. And different angles would have some of those curves changing too.

Every sound source in real life is still going to be what it is. And we humans learn from experience. Whatever pattern keeps coming up over and over again, will be treated as the norm, the one "true" way it should be. It's not so much about hearing right, as it is a cognitive result.
From habit we've become perfectly fine with calling something flat that we don't actually perceive as having the same loudness at each frequency.

A good example to illustrate the difference would be speakers. When we calibrate them in a studio, we'll work on them being flat with a measurement microphone at a fairly short distance. We look for similar SPL values over frequencies at the measured spot. So something close to factual flat source.
What we're going to perceive as audio comes from those speakers is how that fairly flat response is changed by our body, plus whatever hearing damage we already suffer from. So, not flat. And yet the vast majority of listeners will recognize that as neutral, and will find that it is their preferred frequency response on those speakers. Because the response is most in agreement with our daily experience of sound sources. And an instrument played back on those speakers will sound close to what we know that instrument to sound like.
Now take your 2 tones approach and apply it to those speakers. You'll end up with a non flat result, as what you're actually hearing is a sum of effects applied to what was a flat tuning. Including the impacts listed in the graph above. On a really neutral speaker, let's say in an anechoic chamber so we don't bother with room acoustic for now, you will hear a 70dB, 4kHz tone louder than a 70dB, 60Hz tone. But because you've heard everything with that "body filter" applied your entire life, if you compensate for it, that's when things won't sound normal to you.



Now it gets complicated because of headphones:
a headphone is really troublesome in term of what objectively should be the target, because it piles up several significant issues that are likely to ruin any chance of subjectively perceiving something we could identify as the norm:
-The sound turns with the head.
-Most audio was made for speaker playback, expecting room acoustic, reverb and the left ear getting sound from the right speaker.
-The sound source bypasses the head and torso, to send sound right into the ears from more or less a 90° angle. That will be great to listen to people whispering in our ears, but for every sound source supposed to be at some distance in front of us, our brain will expect the impact of the head, torso and outer ear for that direction. And it typically won't get it.
And of course for low frequencies, we're missing tactile feeling from the body being shaken.

All those reasons are why on headphones, not only music tends to feel in our head with strong lateralization, but why it rarely feels flat. Because the right tuning(and it's arguable that there is one for non binaural recordings), for one listener will not be right for another one with a different body. This time, unlike with speakers where we don't have to care about body differences because each listener will apply his own body filter like he always does on all sounds, with headphone we need something that will also mimic the missing part of the body filter. the part we're missing thanks to the headphone being right on our ears.
So overall it's a fact that we do need a custom tuning on headphone. But even then, because of the other factors telling our brain how the situation is not that of a normal sound source at a distance, it's likely that even the acoustically correct frequency response with the right audio track, wouldn't be enough to "feel right" the way we might with speakers, and the way we absolutely will with real instruments playing in front of us. That IMO is what makes EQing a headphone somewhat harder than doing it with speakers. Because for some people, going with what feels right might never yield a result. And worst, some might overcompensate in various areas for the wrong reasons because the brain keeps telling them that something is missing even though it's unrelated to FR. Like how we often boost the bass too much intuitively trying to get our missing tactile feeling back.

In any case, equal loudness contour from pure tones can be a tool to find a reference, like if you're trying to match the FR of 2 sound sources. then you could EQ both sources for equal loudness with tones like you suggested, and then use the 2 EQ curves to find out how to match one source to the other. Like with 2 headphones, or one headphone and one pair of speakers. That's what I was talking about in my previous post when suggesting some possible approach. But it's not perfect. Nothing is when we don't first fix the other issues of headphone playback.
Now, just tuning a given headphone or anything else for that matter, so that each tone sounds equally loud like you suggested, that will never give you the right tuning. Not objectively, not subjectively. That change is baked in us, and when you EQ for equal loudness contour, you try to oppose a lifetime of experience. That won't feel right.
 

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